Residuals The hat matrix Pearson residuals The rst kind is called the Pearson residual, and is based on the idea of subtracting o the mean and dividing by the standard deviation For a logistic regression model, r i= y i ˇ^ i p ˇ^ i(1 ˇ^ i) Note that if we replace ˇ^ iwith ˇ i, then r ihas mean 0 and variance 1 Patrick Breheny BST 760: Advanced Regression 5/24
We can use CORREL Function to calculate coefficient of correlation. Syntax of CORREL CORREL(array1, array2) array1 is the range of variable x, while array2 is the range of variable y. Example. Correlation =CORREL(B2:B4,C2:C4) = 0.944911183
Pearson’s r measures the strength of the linear relationship between two variables. Pearson’s r is always between -1 and 1. Here is a perfect positive relationship. r is equal to 1.0: This residual is heteroscedastic from (2.3), and a standardized residual may be preferred. The two standard choices are Pearson and deviance residuals, with associated measures of goodness of fit being Pearson's statistic and the deviance. The Pearson residual is the obvious standardized residual pyii=−ii ∧∧ ()/µµ12/. (2.6)
TI-84 Video: Residuals and Residual Plots (YouTube) (Vimeo). TI-84 Graphing Calculator. CPM Core Connections eTools & Videos. CC Course 1 eTools.
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